Compressing Θ-Chain in Slit Geometry

Abstract

When compressed in a slit of width D, a Θ-chain that displays the scaling of size R 0 (diameter) with respect to the number of monomers N , R 0 ∼ aN 1/2 , expands in the lateral direction as R ∼ aN ν (a/D) 2ν−1 . Provided that the Θ condition is strictly maintained throughout the compression, the well-known scaling exponent of Θ-chain in 2 dimensions, ν = 4/7, is anticipated in a perfect confinement. However, numerics shows that upon increasing compression from R 0 /D < 1 to R 0 /D 1, ν gradually deviates from ν = 1/2 and plateaus at ν = 3/4, the exponent associated with the self-avoiding walk in two dimensions. Using both theoretical considerations and numerics, we argue that it is highly nontrivial to maintain the Θ condition under confinement because of two major effects. First, as the dimension is reduced from 3 to 2 dimensions, the contributions of higher order virial terms, which can be ignored in 3 dimensions at large N , become significant. Second and more importantly, the geometrical confinement, which is regarded as an applied external field, alters the 1 arXiv:1905.13473v1 [cond-mat.soft] 31 May 2019 second virial coefficient (B 2 ) changes from B 2 = 0 (Θ condition) in free space to B 2 > 0 (good-solvent condition) in confinement. Our study provides practical insight into how confinement affects the conformation of a single polymer chain.

Statistical Properties of a Slit-Confined Wormlike Chain of Finite Length

“…A recent theoretical and computer simulation study has pointed out other peculiar conformational properties when a single long polymer is compressed from 3D to 2D. 83 The simulation condition of the polymer is prepared at the Θ-condition in 3D, where the repulsive excluded volume and attractive interaction well compensate each other at the second-virial level. As such, the conformation of the polymer in 3D follows the randomwalk scaling, equivalent to that of an ideal chain.…”

“…The theoretical concept of no excluded volume is usually associated with a real polymer at the Θ-condition. A recent theoretical and computer simulation study has pointed out other peculiar conformational properties when a single long polymer is compressed from 3D to 2D . The simulation condition of the polymer is prepared at the Θ-condition in 3D, where the repulsive excluded volume and attractive interaction well compensate each other at the second-virial level.…”

Near-Θ Polymers in a Cylindrical Space

“…The value of v is controlled by the quality of the solvent and is related to the second virial coefficient of monomers B 2 as v = 2 B 2 . In a strict-Θ solvent, v vanishes; higher-order interactions give rise to a logarithmic correction to chain sizes. , More practically, in a near-Θ solvent, v ≈ 0. In this case, the notion of thermal blobs is useful: inside a thermal blob, self-avoidance is insignificant (see Figure , where the thermal blob is represented by the dashed circles in red).…”

“…The dashed circles in red represent the thermal blob, inside which self-avoidance is insignificant. Confinement increases self-avoidance, as if it changes the solvent quality, turning the near-Θ solvent into a good solvent, as detailed in Figures – (see ref for the slit confinement). The stronger the confinement is, the stronger the self-avoidance is and the smaller the thermal blob size ξ T is.…”

“…In a conventional picture, v depends on the temperature, but its dependence on other external parameters, such as confinement, has often been under-appreciated. , A recent study, however, suggests that the second virial coefficient of a Θ polymer becomes positive in a slit confinement …”